We study how the skill distribution in an economy responds to changes in wage gaps induced by trade integration. Using administrative data for Denmark (1993-2012), we conduct a two-step empirical analysis. In the first step, we predict changes in wage gaps that are triggered by exogenous trade shocks. In the second step, we estimate the impact of such changes on the skill distribution. The main results for Denmark show that both the average and the standard deviation of skills increase as a result of trade integration. We then extend our analysis to Portugal, using its administrative data (1993-2012), to shed light on the potential role the labor market and education policy may play in establishing the feedback effect of trade on the skill distribution. Finally, we provide a theoretical intuition to rationalize both sets of results.